Embodied Technical Progress In A Multi Sectoral Economic Growth Model

The effect of vintage of capital on a multi-sectoral economic growth model is examined. First, the author extends the substitution theorem to a dynamic system where various capital goods are classified not only in terms of their kinds but also in terms of their vintages. With no joint production, each commodity is assumed to have a Cobb-Douglas type of production function which is identical for all different vintages of its capital goods. In a steady-state equilibrium, capital-output ratios (in efficiency units when involving the capitalaugmenting technical progress) turn out to be invariant for individual vintages. It is also shown that all capitaland labor-output ratios in the economy take simple and easily calculated functions of only the interest rate and the trend values of technology. Current flow requirements per output, defined as depreciated part of capital goods, vary over time along with the distribution of their vintages. However, in a steady-state equilibrium they take invariant values in the case of no technological change. Second, the author is concerned with the existence of a unique balanced growth of production in our multi-sectoral model, which turns out to be a variant of the dynamic Leontief model. Making use o f the Hawkins-Simon conditions and the Frobenius theorem, we prove the existence of the balanced growth in abstraction from technological change, as well as in the case of technical progress. (Author).